In reply to climbingrose:
Try climbing tape.
When i'm training on my overhanging wall i tend to get sore skin on any finger, not directly the joint but the bit of finger either side of it. If i tape it, it holds everything together. What i usually do is a couple of moves, identify which finger sections are giving my jip and put tape over them. It varies every time, probably related to specific arm and hand strength on any given night.
Also - as the strength in your hands and arms improves, your hand skin will hurt less. It hurts because of very slight movement between the hold and your hand, a result of reduced friction because your grip is not mundo hardcore. When you get stronger, you'll grip harder and your hands will hurt less.